Abstract:

A method for calibrating a dual-energy CT system and an image
reconstruction method are disclosed to calculate images of atomic number
and density of a scanned object as well as its attenuation coefficient
images at any energy level. The present invention removes the effect from
a cupping artifact due to X-ray beam hardening. The method for
calibrating a dual-energy CT system is provided comprising steps of
selecting at least two different materials, detecting penetrative rays
from dual-energy rays penetrating said at least two different materials
under different combinations of thickness to acquire projection values,
and creating a lookup table in a form of correspondence between said
different combinations of thickness and said projection values. The image
reconstruction method is provided comprising steps of scanning an object
with dual-energy rays to acquire dual-energy projection values,
calculating projection values of base material coefficients corresponding
to said dual-energy projection values based on a pre-created lookup
table, and reconstructing an image of base material coefficient
distribution based on said projection values of base material
coefficients. In this way, images of atomic number and density of an
object as well as its attenuation coefficient images can be calculated
from the images of the distribution of base material coefficients.
Compared with the prior art technique, the method proposed in the present
invention has advantages of simple calibration procedure, high
calculation precision and invulnerability to X-ray beam hardening.

Claims:

1. A method for calibrating a dual-energy CT system comprising the steps
of:selecting at least two different materials;detecting penetrative rays
from dual-energy rays penetrating said at least two different materials
under different combinations of thickness to acquire projection values;
andcreating a lookup table in a form of correspondence between said
different combinations of thickness and said projection values.

3. The method of claim 2, wherein said low- and high-energy rays are
X-rays.

4. The method of claim 1, wherein said at least two different materials
comprises carbon and aluminum.

5. An image reconstruction method comprising the steps of:scanning an
object under inspect with dual-energy rays to acquire dual-energy
projection values;calculating projection values of base material
coefficients corresponding to said dual-energy projection values based on
a pre-created lookup table; andreconstructing an image of base material
coefficient distribution based on said projection values of base material
coefficients.

6. The image reconstruction method of claim 5, further comprises a step of
calculating the atomic number image of said object based on said image of
base material coefficient distribution.

7. The image reconstruction method of claim 5, further comprises step of
calculating the characteristic density image of said object based on said
image of base material coefficient distribution.

8. The image reconstruction method of claim 5, further comprises step of
calculating the attenuation coefficient image of said object based on
said image of base material coefficient distribution.

9. The image reconstruction method of one of claims 5, wherein said lookup
table is created by selecting at least two different materials, detecting
penetrative rays from dual-energy rays penetrating said at least two
different materials under different combinations of thickness to acquire
projection values, and creating a lookup table in a form of
correspondence between said different combinations of thickness and said
projection values.

Description:

BACKGROUND OF THE INVENTION

[0001]1. Field of Invention

[0002]The present invention relates to radiography technology, in
particular to a method for calibrating a dual-energy CT system and a
corresponding image reconstruction method, which can eliminate a cupping
artifact caused by X-ray beam hardening.

[0003]2. Description of Prior Art

[0004]As technology progresses, Computerized Tomography (CT) technique has
been applied to systems for inspecting tourists' luggage. In the
widely-used CT technique, an X-ray is utilized as a ray source which
generates X-rays of continuous energy distribution. An image obtained by
the conventional image reconstruction method represents the attenuation
coefficient distribution of an object, which will give rise to a cupping
artifact if affected by X-ray beam hardening.

[0005]In the existing algorithm of dual-energy CT image reconstruction,
images of high- and low-energy attenuation coefficients for an object are
first acquired using a conventional CT reconstruction method, and then
calculation is made to obtain density and atomic number images. Such
existing method cannot eliminate the cupping artifact due to hardening of
rays and thus results in an inaccurate calculation result as well as
reduced accuracy in material identification.

SUMMARY OF THE INVENTION

[0006]The present invention is made to address the above problems. One
object of the present invention is to provide a method for calibrating a
dual-energy CT system and an image reconstruction method. In the present
invention, a dual-energy lookup table can be obtained by selecting base
materials, fabricating a step-shaped block and rectangular blocks having
a series of thickness and measuring projection values under different
combinations of thickness, in order to implement system calibration.
Further, after the calibration of the dual-energy CT system utilizing two
types of base materials, a dual-energy CT reconstruction algorithm can be
adopted to acquire images of atomic number and density of an object as
well as its attenuation coefficient images at any energy level.

[0007]According to an aspect of the present invention, a method for
calibrating a dual-energy CT system is provided comprising the steps of
selecting at least two different materials, detecting penetrative rays
from dual-energy rays penetrating the at least two different materials
under different combinations of thickness to acquire projection values,
and creating a lookup table in a form of correspondence between the
different combinations of thickness and the projection values.

[0010]Preferably, the at least two different materials comprises carbon
and aluminum.

[0011]According a further aspect of the present invention, an image
reconstruction method is provided comprising steps of scanning an object
under inspect with dual-energy rays to acquire dual-energy projection
values, calculating projection values of base material coefficients
corresponding to the dual-energy projection values based on a pre-created
lookup table, and reconstructing an image of base material coefficient
distribution based on the projection values of base material
coefficients.

[0012]Preferably, the image reconstruction method further comprises a step
of calculating the atomic number image of the object based on the image
of base material coefficient distribution.

[0013]Preferably, the image reconstruction method further comprises a step
of calculating the characteristic density image of the object based on
the image of base material coefficient distribution.

[0014]Preferably, the image reconstruction method further comprises step
of calculating the attenuation coefficient image of the object based on
the image of base material coefficient distribution.

[0015]Preferably, the lookup table is created by selecting at least two
different materials, detecting penetrative rays from dual-energy rays
penetrating the at least two different materials under different
combinations of thickness to acquire projection values, and creating a
lookup table in a form of correspondence between the different
combinations of thickness and the projection values.

[0016]Compared with the prior art technique, the method proposed in the
embodiments of the present invention has advantages of simple calibration
procedure, high calculation precision and invulnerability to X-ray beam
hardening.

[0017]Images reconstructed by the method in accordance with the
embodiments of the present invention can serve as evidence in determining
substance properties in security inspection in order to improve accuracy
of security inspection.

[0018]Image reconstruction results obtained by the method of the present
invention have a higher precision, and the resulting atomic number and
density values each have an error within 1% according to simulation
results.

[0019]According to the present invention, it is possible to acquire the
attenuation coefficient image of the object at any energy level with no
effect from X-ray spectrum hardening.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]The above advantages and features of the present invention will be
apparent from the following detailed description taken conjunction with
the drawings in which:

[0021]FIG. 1 is a schematic diagram of a dual-energy CT system according
to an embodiment of the present invention;

[0022]FIG. 2 is a schematic diagram for explaining a method for
calibrating a dual-energy CT system according to an embodiment of the
present invention;

[0023]FIG. 3 is a flowchart depicting a method for calibrating a
dual-energy CT system and an image reconstruction method according to an
embodiment of the present invention;

[0024]FIG. 4 is a schematic cross-sectional diagram of an organic glass
bottle full of water;

[0025]FIG. 5 shows resulting images reconstructed by the prior art method
and by the method of the present invention, in which FIG. 5A is a
low-energy attenuation coefficient image reconstructed by a conventional
method, FIG. 5B is attenuation coefficient image at 60 keV obtained by
the image reconstruction method of the present invention, and the display
gray windows for the images in FIGS. 5A and 5B are [0.12 0.21]; FIG. 5C
is a characteristic density image reconstructed by the method of the
present invention, with a display gray window of [0.6 1.12]; FIG. 5C is
an atomic number image reconstructed by the method of the present
invention, with a display gray window of [6 8]; FIGS. 5E and 5F indicate
respectively curves of pixel values extracted along the central lines of
the images shown in FIGS. 5A and 5B; FIGS. 5G and 5H indicate
respectively curves of pixel values extracted along the central lines of
the images shown in FIGS. 5C and 5D versus a curve for an actual image,
where solid lines denote reconstruction results, and dashed lines denote
actual values.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026]Now, a detailed description will be given to the preferred
embodiments of the present invention with reference to the figures,
throughout which like reference signs denote identical or similar
component, though illustrated in different figures. For clarity and
conciseness, specific description of any known function or structure
incorporated here will be omitted otherwise the subject of the present
invention may be obscured.

[0027]Mathematic Principle for CT

[0028]Subjecting a 2D distribution u(x,y) to line integration along a
direction θ will result in a 1D function p.sub.θ(t) which is
referred to as the projection of u(x,y) at an angle of θ. If the
projection p.sub.θ(t) along all directions can be obtained, the 2D
distribution u(x,y) can be calculated accurately based on Radon
transformation. The procedure of deriving a 2D distribution from its
projection is called reconstruction, which acts as the mathematic
principle for CT.

[0029]In practice, after an X-ray and a detector go round an object for
one cycle, there measured and obtained the projections of the attenuation
coefficient distribution along all directions for some slice of the
object, and the 2D distribution of attenuation coefficients of the object
slice can be reconstructed on the basis of the CT principle.

[0030]Base Material Decomposition Model

[0031]Within an energy range (<200 keV) involved in a small-sized X-ray
security inspection system, the linear attenuation coefficient of a
material can be approximated with the following analytic expression (1):

In which fp(E) represents variation in photoelectric effect cross
section over different energy levels, fKN(E) represents variation in
Compton scatter cross section over different energy levels, and each of
fp(E) and fKN(E) has a known analytic expression. Further,
variables a1 and a2 depend on the atomic number, mass number
and density of the material and are expressed as (2) and (3),
respectively, with Z denoting atomic number, M denoting mass number,
ρ denoting density (g/cm3), and n is a constant.

[0032]Since the linear attenuation coefficient of each material can be
uniquely determined by the two coefficients, a1 and a2, in the
expression (1), two base materials, such as carbon and aluminum, can be
selected so as to represent the linear attenuation coefficient of any
other material with a linear combination of the linear attenuation
coefficients of these base materials, as illustrated in the expression
(4):

(E)=b1μ1(E)+b2μ2(E) (4)

In which μ(E) denotes the linear attenuation coefficient of one
arbitrary material of an object under inspect, μ1(E) and
μ2(E) are the linear attenuation coefficients of the selected
base material, b1 and b2 are called base material coefficients.

[0033]Following the expression (5), the characteristic density is defined
as a product of density and a ratio between atomic number multiplied by 2
and mass number:

ρ * = ρ 2 Z M ( 5 )

Given that the atomic numbers and characteristic densities of the two base
material are (Z1,ρ*1) and (Z2,ρ*2),
respectively, the atomic number and characteristic density of any other
material can be derived from the above expressions (1)˜(4), as
illustrated by the expressions (6) and (7):

[0035]The X-ray tube generally creates an energy spectrum as a continuous
spectrum, and the energy response function of the detector to X-rays is
not constant. Given as the product of energy spectrum and energy response
function, and being normalized as

∫ 0 E m S ( E ) E = 1 ( 8 )

[0036]the projection value along a projection line is expressed as the
following integral:

in which I0 and I represent the read values of the detector before
and after the attenuation of rays by the object, respectively, Em
represents the maximum energy of the rays, and l represents the path the
rays travel through.

[0037]The expression (9) reveals the relation between the projection value
p measured actually by the system and the 2D distribution μ(x,y). It
is obvious that, due to the polyenergetic characteristic of X-rays, the
expression (9) does not represents the line integral of μ(x,y) along a
line and thus cannot satisfy the mathematic principle for CT. Since the
conventional reconstruction algorithm neglects such inconsistence, the
reconstructed image for μ(x,y) contains a cupping artifact referred to
as beam hardening artifact.

[0038]The typical existing dual-energy CT method first utilizes the
conventional reconstruction algorithm to acquire two sets of μ(x,y),
and then calculates such information as atomic number and density. Such
method cannot remove the effect imposed by the polyenergetic
characteristic of rays. In contrast, the present invention addresses this
problem with the concept of base material decomposition.

[0039]Substituting a base material decomposition model into the expression
(9) results in a projection value based on base material coefficient,
which is expressed as:

[0040]The integration along the path l in the expression (10) can be
written into the expressions (11) and (12):

∫ l b 1 ( x , y ) l = B 1 ( 11
) ∫ l b 2 ( x , y ) l = B 2
( 12 )

[0041]In this way, B1 and B2 are called projection values of
base material coefficients according to the definition of the expressions
(11) and (12). Assume that we have acquired complete project values from
all angles for these base material coefficients, the distribution of the
base material coefficients b1 and b2 can be obtained according
to the CT reconstruction theory, and thus the distribution of atomic
number and characteristic density of the object as well as the linear
attenuation coefficient at any energy level can be calculated from the
base material decomposition model.

[0042]Calculation of Projection Values of Base Material Coefficient

[0043]Having acquired the projection data at two different energy levels,
the dual-energy CT obtains the dual-energy projection data as follows:

[0044]Although, in theory, (B1,B2) can be found out from the
expressions (13) and (14) after the measurement of (p1,p2),
both of the above expressions cannot be solved analytically since they
are logarithmic integration equations. Besides, the frequently-used
nonlinear iterative solution requires a huge computation and has
difficulty in finding a stable result.

[0045]The present inventor has noticed that, after the rays travel through
the first base material of thickness d1 and d2 the second base
material of thickness, the measured dual-energy projection data have the
form of the following expressions (15) and (16):

[0046]As can be seen from the comparison between (13) (14) and (15) (16),
the pair of projection values (B1,B2) for base material
coefficients will be exactly the same as the thickness combination
(d1,d2) of the base material if the measured pair of projection
data (p1,p2) is identical to
{p1(B1,B2),p2(B1,B2)}.

[0047]Therefore, by measuring dual-energy projections of known materials
with different combinations of thickness, the correspondence between the
pair of dual-energy projection data (p1,p2) and the pair of
projection values (B1,B2) of base material coefficients can be
acquired, and thus the lookup table can be created.

[0048]During image reconstruction, the pair of dual-energy projection data
(p1,p2) is measured by scanning the object with dual-energy
rays. Then, the lookup table is searched for the corresponding pair of
projection values (B1,B2) of base material coefficients based
on the pair of dual-energy projection data (p1,p2).
Alternatively, if only an approximate pair of projection values
(B'1,B'2) of base material coefficients is found, the above
pair of projection values (B1,B2) of base material coefficients
can be acquired by means of linear interpolation. Apparently, such
calculation is much easier than that of solving a logarithmic equation.

[0049]FIG. 1 is a schematic diagram of a dual-energy CT system according
to an embodiment of the present invention. As shown in FIG. 1, a ray
source 100 generates dual-energy X-rays having a continuous energy
distribution at predefined timing under the control of a controller 500.
The object 200 is placed on a bearing mechanism 300, which can rotate
uniformly and be lifted up and down under the control of the controller
500. An array of detectors 400 is arranged at a position opposite to the
ray source 100, and receives the penetrative rays, which have traveled
through the object 200, under the control of the controller 500 so as to
obtain detection signals for a first energy level and detection signals
for a second energy level. The signals detected by the detector array 400
are converted into digital signals and stored in a computer 600 for
subsequent processing of calibration or reconstruction.

[0050]FIG. 2 is a schematic diagram for explaining a method for
calibrating a dual-energy CT system according to an embodiment of the
present invention. FIG. 2 shows a two-layer structure used by the
detector array, with a low-energy thinner crystal 410 being placed before
a high-energy thicker crystal 420, the former mainly absorbing the
low-energy portion of X-rays and the latter mainly absorbing the
high-energy portion of X-rays. Signals detected by the low-energy and
high-energy crystals 410 and 420 are converted into digital signals by an
auxiliary circuit, such as A/D converter. In this way, the detector array
400 can output high- and low-energy signals separately.

[0051]FIG. 3 is a flowchart depicting a method for calibrating a
dual-energy CT system and an image reconstruction method according to an
embodiment of the present invention. The left part of FIG. 3 illustrates
the procedure of calibrating the dual-energy CT system, and the right
part illustrates the detail of the image reconstruction method.

[0052]Two types of common materials, such as carbon and aluminum, are
selected as base materials X and Y in FIG. 2 (S110). One of the base
materials, for example, carbon X, is formed in a step-shape, and the
other base material, aluminum Y here, is used to make cuboids of various
thickness. A corresponding pair of low- and high-energy projection values
(p1,p2) can be measured based on each pair of thickness values
(d1,d2) for the base materials.

[0053]With the geometrical arrangement in FIG. 2, the detector array 400
can measure and obtain dual-energy projection values corresponding to the
combination of certain thickness of the base material Y and a serial of
thickness of the base material X, respectively, while the base materials
pass through the radiation area from top to bottom. The thickness of the
base material Y is then changed, and the above measurement is repeated to
obtain the dual-energy projection values of X and Y for respective
combinations of thickness. All of the measurement results constitute the
correspondence between the dual-energy projection values and the
combinations of thickness for the base materials (S120).

[0054]In the process of inspection, the object is first placed on the
bearing mechanism 300. Then, the controller 500 controls the ray source
200 to emit dual-energy X-rays, which radiate the object from all angles,
and the pairs of dual-energy projection values are obtained by the
detector array 400 (S210).

[0055]Next, the lookup table created above is utilized to compute a
thickness combination (d1,d2) corresponding to each of the
pairs of dual-energy projection values, and thus a pair of projection
values (B1,B2) of the base material coefficients can be found
(S220). Subsequently, an image of the distribution of the base material
coefficients b1 and b2 can be acquired according to the CT
reconstruction algorithm (S230).

[0056]Further, the obtained image of the base material coefficients is
used to calculate the atomic number and characteristic density image of
the object as well as its attenuation coefficient image at any energy
level (S240).

[0057]The following numerical simulation experiment is conducted to verify
the above reconstruction method. Given that the X-ray has a high voltage
of 140 kV and the detector array uses CsI crystal, the energy spectrum
and the energy response function of the detector are first simulated
through Monte Carlo method, and the dual-energy projection values is
computed analytically with the expression (9).

[0058]For example, carbon and aluminum are chosen as base materials, with
atomic numbers being 6 and 13, mass numbers being 12.011 and 26.9815,
densities being 1 g/cm3 and 2.7 g/cm3, and characteristic
densities being 0.999084 g/cm3 and 2.601783 g/cm3,
respectively. The material of carbon has a serial of thickness from 0 to
10 cm with an interval of 1 cm, and the material of aluminum has a serial
of thickness from 0 to 1 cm with an interval of 0.1 cm. The expressions
(15) and (16) are adopted to calculate dual-energy projection values for
different combinations of thickness. Here, each of carbon and aluminum
has 11 types of thickness, and thus a lookup table is formed with a size
of 11×11.

[0059]FIG. 4 is a schematic cross-sectional diagram of an organic glass
bottle full of water. The organic glass bottle full of water is used as
the object, with its side wall having a thickness of 5 mm, the outer
diameter being 160 mm and the inner diameter being 150 mm. Organic glass
has atomic number of 6.56, density of 0.8 g/cm3 and characteristic
density of 0.863 g/cm3. Water has atomic number of 7.51, density of
1.0 g/cm3 and characteristic density of 1.11 g/cm3.

[0060]In CT scanning, parallel beam scanning is used. The number of
projection angles is 720, the number of detectors is 512, and the size of
a reconstructed image is 512×512.

[0061]FIG. 5 shows the resulting images reconstructed by the prior art
method and by the method of the present invention, in which FIG. 5A is a
low-energy attenuation coefficient image reconstructed by a conventional
method, FIG. 5B is attenuation coefficient image at 60 keV obtained by
the image reconstruction method of the present invention, and the display
gray windows for the images in FIGS. 5A and 5B are [0.12 0.21]; FIG. 5C
is a characteristic density image reconstructed by the method of the
present invention, with a display gray window of [0.6 1.12]; FIG. 5C is
an atomic number image reconstructed by the method of the present
invention, with a display gray window of [6 8]; FIGS. 5E and 5F indicate
respectively curves of pixel values extracted along the central lines of
the images shown in FIGS. 5A and 5B; FIGS. 5G and 5H indicate
respectively curves of pixel values extracted along the central lines of
the images shown in FIGS. 5C and 5D versus a curve for the actual values,
where solid lines denote reconstruction results, and dashed lines denote
actual values.

[0062]As can be seen from the comparison between FIGS. 5A and 5B as well
as FIGS. 5C and 5D, the cupping artifact due to X-ray beam hardening can
be removed from the attenuation coefficient images obtained through the
method of the present embodiment. Furthermore, as shown in FIGS. 5G and
5H, the reconstruction results have little difference from the actual
values, thereby suggesting that a higher precision can be achieved by the
method according to the present invention.

[0063]In summary, the calibration method according to the embodiments of
the present invention has a reduced complexity. To be specific, a
dual-energy lookup table can be obtained by selecting base material,
fabricating a step-shaped block and rectangular blocks having a series of
thickness and measuring projection values under different combinations of
thickness, in order to implement system calibration.

[0064]In addition, with the image reconstruction method according to the
embodiments of the present invention, the obtained reconstruction result
has a high precision. As can be seen from the simulation result, the
values of atomic number and density have an error within 1%.

[0065]Further, with the method of the present invention, it is possible to
acquire the attenuation coefficient image of the object at any energy
level without any effect from X-ray beam hardening.

[0066]The foregoing description is only intended to illustrate the
embodiments of the present invention other than limiting the present
invention. For those skilled in the art, any change or substitution that
can be made readily within the scope of the present invention should be
encompassed by the scope of the present invention. Therefore, the scope
of the present invention should be defined by the claims.